Evaluate the definite integral. $\int^{16}_{4}\left(3\sqrt{x}\right)\,dx = $
Answer: First, use the power rule: $\begin{aligned}\int^{16}_{4}\left(3\sqrt{x}\right)\,dx ~&=~\int^{16}_{4}\left(3x^{\frac12}\right)\,dx \\&=(2x^\frac32)\Bigg|^{16}_{4}\end{aligned}$ Second, plug in the limits of integration: $(2\cdot{16}^{\frac32})-(2\cdot4^{\frac32}) = 128-16 = 112$. The answer: $\int^{16}_{4}\left(3\sqrt{x}\right)\,dx ~=~112$